Problem: Solve for $x$ : $8\sqrt{x} + 1 = 6\sqrt{x} + 6$
Subtract $6\sqrt{x}$ from both sides: $(8\sqrt{x} + 1) - 6\sqrt{x} = (6\sqrt{x} + 6) - 6\sqrt{x}$ $2\sqrt{x} + 1 = 6$ Subtract $1$ from both sides: $(2\sqrt{x} + 1) - 1 = 6 - 1$ $2\sqrt{x} = 5$ Divide both sides by $2$ $\frac{2\sqrt{x}}{2} = \frac{5}{2}$ Simplify. $\sqrt{x} = \dfrac{5}{2}$ Square both sides. $\sqrt{x} \cdot \sqrt{x} = \dfrac{5}{2} \cdot \dfrac{5}{2}$ $x = \dfrac{25}{4}$